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How to Think Like a Computer Scientist

Chapter 2

Variables, expressions and statements

2.1 Values and types

A value is one of the fundamental things like a letter or a
number that a program manipulates. The values we have seen so far
are 2 (the result when we added 1 + 1), and
'Hello, World!'.

These values belong to different types:
2 is an integer, and 'Hello, World!' is a string,
so-called because it contains a "string" of letters.
You (and the interpreter) can identify
strings because they are enclosed in quotation marks.

The print statement also works for integers.

>>> print 4
4

If you are not sure what type a value has,
the interpreter can tell you.

>>> type('Hello, World!')
<type 'str'>
>>> type(17)
<type 'int'>

Not surprisingly, strings belong to the type str and
integers belong to the type int. Less obviously, numbers
with a decimal point belong to a type called float,
because these numbers are represented in a
format called floating-point.

>>> type(3.2)
<type 'float'>

What about values like '17' and '3.2'?
They look like numbers, but they are in quotation marks like
strings.

>>> type('17')
<type 'str'>
>>> type('3.2')
<type 'str'>

They're strings.

When you type a large integer, you might be tempted to use commas
between groups of three digits, as in 1,000,000. This is not a
legal integer in Python, but it is a legal expression:

>>> print 1,000,000
1 0 0

Well, that's not what we expected at all! Python interprets 1,000,000 as a comma-separated list of three integers, which it
prints consecutively. This is the first example we have seen of a
semantic error: the code runs without producing an error message, but
it doesn't do the "right" thing.

2.2 Variables

One of the most powerful features of a programming language is the
ability to manipulate variables. A variable is a name that
refers to a value.

The assignment statement creates new variables and gives
them values:

>>> message = "What's up, Doc?">>> n = 17
>>> pi = 3.14159

This example makes three assignments. The first assigns the string
"What's up, Doc?" to a new variable named message.
The second gives the integer 17 to n, and the third
gives the floating-point number 3.14159 to pi.

Notice that the first statement uses double quotes to enclose the
string. In general, single and double quotes do the same thing, but
if the string contains a single quote (or an apostrophe, which is
the same character), you have to use double quotes to enclose it.

A common way to represent variables on paper is to write the name with
an arrow pointing to the variable's value. This kind of figure is
called a state diagram because it shows what state each of the
variables is in (think of it as the variable's state of mind).
This diagram shows the result of the assignment statements:

The print statement also works with variables.

>>> print message
What's up, Doc?
>>> print n
17
>>> print pi
3.14159

In each case the result is the value of the variable.
Variables also have types; again, we can ask the
interpreter what they are.

2.3 Variable names and keywords

Programmers generally choose names for their variables that
are meaningful they document what the variable is used for.

Variable names can be arbitrarily long. They can contain
both letters and numbers, but they have to begin with a letter.
Although it is legal to use uppercase letters, by convention
we don't. If you do, remember that case matters. Bruce
and bruce are different variables.

The underscore character (_) can appear in a name.
It is often used in names with multiple words, such as
my_name or price_of_tea_in_china.

When the Python interpreter displays the value of an expression, it
uses the same format you would use to enter a value. In the case of
strings, that means that it includes the quotation marks. But if
you use a print statement, Python displays the contents of the string
without the quotation marks.

In a script, an expression all by itself is a legal statement, but it
doesn't do anything. The script

17
3.2
'Hello, World!'1 + 1

produces no output at all. How would you change the script to
display the values of these four expressions?

2.6 Operators and operands

Operators are special symbols that represent computations
like addition and multiplication. The values the operator uses are
called operands.

The following are all legal Python expressions whose meaning is more or
less clear:

20+32 hour-1 hour*60+minute minute/60 5**2 (5+9)*(15-7)

The symbols +, -, and /, and the use of parenthesis for
grouping, mean in Python what they mean in mathematics. The asterisk
(*) is the symbol for multiplication, and ** is the symbol
for exponentiation.

When a variable name appears in the place of an operand, it
is replaced with its value before the operation is
performed.

Addition, subtraction, multiplication, and exponentiation all do what
you expect, but you might be surprised by division. The following
operation has an unexpected result:

>>> minute = 59
>>> minute/60
0

The value of minute is 59, and in conventional arithmetic 59
divided by 60 is 0.98333, not 0. The reason for the discrepancy is
that Python is performing integer division.

When both of the operands are integers, the result must also be an integer,
and by convention, integer division always rounds down, even in cases
like this where the next integer is very close.

A possible solution to this problem is to calculate a percentage
rather than a fraction:

>>> minute*100/60
98

Again the result is rounded down, but at least now the answer is
approximately correct. Another alternative is to use floating-point
division, which we get to in Chapter 3.

2.7 Order of operations

When more than one operator appears in an expression, the order of
evaluation depends on the rules of precedence. Python follows
the same precedence rules for its mathematical operators that
mathematics does. The acronym PEMDAS is a useful way to
remember the order of operations:

Parentheses have the highest precedence and can be used
to force an expression to evaluate in the order you want. Since
expressions in parentheses are evaluated first, 2 * (3-1) is 4,
and (1+1)**(5-2) is 8. You can also use parentheses to make an
expression easier to read, as in (minute * 100) / 60, even
though it doesn't change the result.

Exponentiation has the next highest precedence, so
2**1+1 is 3 and not 4, and 3*1**3 is 3 and not 27.

Multiplication and Division have the same precedence,
which is higher than Addition and Subtraction, which also
have the same precedence. So 2*3-1 yields 5 rather than 4, and
2/3-1 is -1, not 1 (remember that in integer
division, 2/3=0).

Operators with the same precedence are evaluated from left to
right. So in the expression minute*100/60, the multiplication
happens first, yielding 5900/60, which in turn yields 98.
If the operations had been evaluated from right to left, the result
would have been 59*1, which is 59, which is wrong.

2.8 Operations on strings

In general, you cannot perform mathematical operations on strings, even
if the strings look like numbers. The following are illegal (assuming
that message has type string):

message-1 'Hello'/123 message*'Hello''15'+2

Interestingly, the + operator does work with strings, although it
does not do exactly what you might expect. For strings, the + operator
represents concatenation, which means joining the two operands by
linking them end-to-end. For example:

fruit = 'banana'bakedGood = ' nut bread'print fruit + bakedGood

The output of this program is banana nut bread. The space
before the word nut is part of the string, and is necessary
to produce the space between the concatenated strings.

The * operator also works on strings; it performs repetition.
For example, 'Fun'*3 is 'FunFunFun'. One of the operands
has to be a string; the other has to be an integer.

On one hand, this interpretation of + and * makes sense by
analogy with addition and multiplication. Just as 4*3 is
equivalent to 4+4+4, we expect 'Fun'*3 to be the same as
'Fun'+'Fun'+'Fun', and it is. On the other hand, there is a
significant way in which string concatenation and repetition are
different from integer addition and multiplication.
Can you think of a property that addition and multiplication have
that string concatenation and repetition do not?

2.9 Composition

So far, we have looked at the elements of a program variables,
expressions, and statements in isolation, without talking about how to
combine them.

One of the most useful features of programming languages is their
ability to take small building blocks and compose them. For
example, we know how to add numbers and we know how to print; it turns
out we can do both at the same time:

>>> print 17 + 3
20

In reality, the
addition has to happen before the printing, so the actions aren't
actually happening at the same time. The point is that any
expression involving numbers, strings, and variables can be used inside a
print statement. You've already seen an example of this:

print'Number of minutes since midnight: ', hour*60+minute

You can also put arbitrary expressions on the right-hand side of an
assignment statement:

percentage = (minute * 100) / 60

This ability may not seem impressive now, but you will see other examples
where composition makes it possible to express complex computations neatly and
concisely.

Warning: There are limits on where you can use certain expressions. For
example, the left-hand side of an assignment statement has to be a
variable name, not an expression. So, the following is illegal:
minute+1 = hour.

2.10 Comments

As programs get bigger and more complicated, they get more difficult to
read. Formal languages are dense, and it is often difficult to look
at a piece of
code and figure out what it is doing, or why.

For this reason, it is a good idea to add notes to your programs to explain
in natural language what the program is doing. These notes are called
comments, and they are marked with the # symbol:

In this case, the comment appears on a line by itself. You can also put
comments at the end of a line:

percentage = (minute * 100) / 60 # caution: integer division

Everything from the # to the end of the line is ignored it
has no effect on the program. The message is intended for the programmer or
for future programmers who might use this code. In this case, it
reminds the reader about the ever-surprising behavior of integer division.

This sort of comment is less necessary if you use the integer division
operation, //. It has the same effect as the division
operator * Note, but it signals that the effect
is deliberate.

percentage = (minute * 100) // 60

The integer division operator is like a comment that says, "I know
this is integer division, and I like it that way!"

2.11 Glossary

value

A number or string (or other thing to be named later)
that can be stored in a variable or computed in an expression.

type

A set of values. The type of a value determines how
it can be used in expressions. So far, the types you have seen are integers
(type int), floating-point numbers (type float),
and strings (type string).

floating-point

A format for representing numbers with fractional
parts.

variable

A name that refers to a value.

statement

A section of code that represents a command or action. So
far, the statements you have seen are assignments and print statements.

assignment

A statement that assigns a value to a variable.

state diagram

A graphical representation of a set of variables and the
values to which they refer.

keyword

A reserved word that is used by the compiler to parse a
program; you cannot use keywords like if, def, and while as
variable names.

operator

A special symbol that represents a simple computation like
addition, multiplication, or string concatenation.

operand

One of the values on which an operator operates.

expression

A combination of variables, operators, and values that
represents a single result value.

evaluate

To simplify an expression by performing the operations
in order to yield a single value.

integer division

An operation that divides one integer by
another and yields an integer. Integer division yields only the
whole number of times that the numerator is divisible by the
denominator and discards any remainder.

rules of precedence

The set of rules governing the order in which
expressions involving multiple operators and operands are evaluated.

concatenate

To join two operands end-to-end.

composition

The ability to combine simple expressions and statements
into compound statements and expressions in order to represent complex
computations concisely.

comment

Information in a program that is meant for other
programmers (or anyone reading the source code) and has no effect on the
execution of the program.

Warning: the HTML version of this document is generated from
Latex and may contain translation errors. In
particular, some mathematical expressions are not translated correctly.